Regarding # 1 : The reason why all sorts of games turn up in several categories is exactly what sourwhatup2 explained... every game has several tags and sub-categories it can be filed under.
ArmorGames uses the same categories that are used allover the internet for specific gaming categories. This makes it easier for a visitor to find the specific game he/she is looking for and wants to play. ;)
Regarding # 2 : Making a separate category for "Tower Defence" games would also mean that it is agreed upon to make one for "Zombie", "Battle", "Space" and/or "War" games... this would mean that the selection bar at the top will become way too crowded.
This is where the section of the "Tag Cloud" (or "Game Tags" as it is called here on ArmorGames) comes into play... this is a quick way to search for games related to a certain word or type of game. It never failed thusfar! =)
Next to that, ArmorGames has already implemented a new feature to the homepage that allows a user to see what a certain game beholds. When you hover over a game thumbnail, you will see a text box popup that tells you what sort of game it is, how many times it was played, how it was rated, etc. etc. This actually makes it much easier to see what the game is and whether you will like it or not. =)